A surjective mapping between compact spaces is
said to be (see [59, Chapter 3 and 4, p. 12-28])
quasi-monotone provided that for each subcontinuum Q of Y
with the nonempty interior the set f-1(Q) has a finite number of
components and f maps each of them onto Q.
Janusz J. Charatonik and Pavel Pyrih 2000-09-21
between compact spaces is
said to be (see [59, Chapter 3 and 4, p. 12-28])
quasi-monotone provided that for each subcontinuum Q of Y
with the nonempty interior the set f-1(Q) has a finite number of
components and f maps each of them onto Q.